1. 8-4 Estimation Sample Size

2. Looking at the error as the limiting factor..
If E is determined to be a certain amount, then by solving the equation

3. Looking at the error as the limiting factor..
If E is determined to be a certain amount, then by solving the equation
for E, it can be seen that
This is for numerical data that has a mean and standard deviation

4. Looking at error as the limiting factor
Of a binomial distribution…using the same idea…

5. Looking at error as the limiting factor
Of a binomial distribution…using the same idea…
and isolating n creates
but…this implies we know p.

6. And if we don’t… Watch some algebra… Completing the square
And since p is between 0 and 1, the maximum overall value of the expression will be….

7. Therefore When we have no estimate for p use
Note: Some books say to take p and q as .5

8. Practice
Suppose a candidate is planning a poll and wants to estimate voter support within 3% with 95% confidence. How large a sample is needed?

9. Round up to be safe
Some books make the suggestion to use the Error equation and use .5 for phat and qhat for a “worst case scenario”.
Notice that this works out the same way:

10. Round up to be safe
Some books make the suggestion to use the Error equation and use .5 for phat and qhat for a “worst case scenario”.
Notice that this works out the same way:
Notice also that you don’t need a numerical formula to solve it. If you know the error formula, you have enough.